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Worksheet: Estimating Square Roots

Q1:

Which of the following numbers is closest to 5?

  • A 1 2 0
  • B 1 0 6
  • C 9 4
  • D 2 4
  • E 8

Q2:

The formula for the area of a square is 𝐴 = 𝑠 2 , where 𝑠 is the side length. Estimate the side length of a square whose area is 74 square inches.

Q3:

Using estimation to determine the values of the square roots to the nearest whole number, order the following in ascending order: 3 8 , 7, 8 8 , 4.

  • A 3 8 , 4 , 7 , 8 8
  • B 8 8 , 7 , 3 8 , 4
  • C 7 , 8 8 , 3 8 , 4
  • D 4 , 3 8 , 7 , 8 8
  • E 4 , 7 , 3 8 , 8 8

Q4:

What is the largest integer 𝑎 such that both 1 𝑎 and 𝑎 4 6 3 are between 0 and 1?

Q5:

The positions of the numbers 1 2 0 , 1 0 2 , and 1 1 1 have been identified on the number line. By considering their size, decide which number is represented by 𝑎 .

  • A 1 1 1
  • B 1 2 0
  • C 1 0 2

Q6:

Given that 𝑥 + and 𝑥 < 1 5 < 𝑥 + 1 , find the value of 𝑥 .

  • A2
  • B4
  • C3

Q7:

Without using a calculator, find two consecutive integers that 1 3 + 6 lies between.

Q8:

Order the following numbers from greatest to least: .

  • A
  • B
  • C
  • D

Q9:

The positions of the numbers 2 4 , 1 7 , 2 2 , and 1 9 have been highlighted on the number line. Which arrow represents the position of 1 9 ?

  • A c
  • B a
  • C d
  • Db

Q10:

Order the following numbers from least to greatest: .

  • A
  • B
  • C
  • D
  • E

Q11:

Estimate 1 2 7 to the nearest whole number.

Q12:

The positions of the numbers 2 4 , 1 7 , 2 2 , and 1 9 have been identified on the number line. Which arrow represents the position of 2 2 ?

  • A b
  • B a
  • C d
  • D c

Q13:

Michael is trying to find which two whole numbers lie on either side of 5 1 . He decides that it will be helpful to use what he has been taught about square numbers.

What is the greatest square number below 51?

What is the smallest square number above 51?

Hence, determine the two consecutive whole numbers that 5 1 lies between.

  • A6 and 9
  • B6 and 8
  • C7 and 8
  • D7 and 9
  • E8 and 9

Q14:

Order the following numbers from greatest to least: .

  • A
  • B
  • C
  • D

Q15:

Find an approximated value of 5 7 4 0 without using a calculator.

  • A47.5 or 47.6
  • B63.3 or 63.4
  • C 4 7 . 5 or 4 7 . 6
  • D 3 2 . 4 or 3 2 . 5
  • E55 or 55.1

Q16:

Find the two consecutive one-decimal-place numbers that 1 5 1 lies between.

  • A12.3, 12.4
  • B12.1, 12.2
  • C12.4, 12.5
  • D12.2, 12.3

Q17:

Estimate 4 3 3 1 0 to the nearest whole number.

Q18:

Estimate the solution of the following equation to the nearest integer: 𝑑 = 6 8 2 .

  • A 𝑑 = 6 8 or 𝑑 = 6 8
  • B 𝑑 = 3 4 or 𝑑 = 3 4
  • C 𝑑 = 3 or 𝑑 = 3
  • D 𝑑 = 8 or 𝑑 = 8